13x+1=14×2

Subtract 14×2 from both sides of the equation.

13x+1-14×2=0

Factor -1 out of 13x+1-14×2.

Reorder the expression.

Move 1.

13x-14×2+1=0

Reorder 13x and -14×2.

-14×2+13x+1=0

-14×2+13x+1=0

Factor -1 out of -14×2.

-(14×2)+13x+1=0

Factor -1 out of 13x.

-(14×2)-(-13x)+1=0

Rewrite 1 as -1(-1).

-(14×2)-(-13x)-1⋅-1=0

Factor -1 out of -(14×2)-(-13x).

-(14×2-13x)-1⋅-1=0

Factor -1 out of -(14×2-13x)-1(-1).

-(14×2-13x-1)=0

-(14×2-13x-1)=0

Factor.

Factor by grouping.

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=14⋅-1=-14 and whose sum is b=-13.

Factor -13 out of -13x.

-(14×2-13x-1)=0

Rewrite -13 as 1 plus -14

-(14×2+(1-14)x-1)=0

Apply the distributive property.

-(14×2+1x-14x-1)=0

Multiply x by 1.

-(14×2+x-14x-1)=0

-(14×2+x-14x-1)=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

-((14×2+x)-14x-1)=0

Factor out the greatest common factor (GCF) from each group.

-(x(14x+1)-(14x+1))=0

-(x(14x+1)-(14x+1))=0

Factor the polynomial by factoring out the greatest common factor, 14x+1.

-((14x+1)(x-1))=0

-((14x+1)(x-1))=0

Remove unnecessary parentheses.

-(14x+1)(x-1)=0

-(14x+1)(x-1)=0

-(14x+1)(x-1)=0

Multiply each term in -(14x+1)(x-1)=0 by -1.

(-(14x+1)(x-1))⋅-1=0⋅-1

Simplify (-(14x+1)(x-1))⋅-1.

Simplify by multiplying through.

Apply the distributive property.

(-(14x)-1⋅1)(x-1)⋅-1=0⋅-1

Multiply.

Multiply 14 by -1.

(-14x-1⋅1)(x-1)⋅-1=0⋅-1

Multiply -1 by 1.

(-14x-1)(x-1)⋅-1=0⋅-1

(-14x-1)(x-1)⋅-1=0⋅-1

(-14x-1)(x-1)⋅-1=0⋅-1

Expand (-14x-1)(x-1) using the FOIL Method.

Apply the distributive property.

(-14x(x-1)-1(x-1))⋅-1=0⋅-1

Apply the distributive property.

(-14x⋅x-14x⋅-1-1(x-1))⋅-1=0⋅-1

Apply the distributive property.

(-14x⋅x-14x⋅-1-1x-1⋅-1)⋅-1=0⋅-1

(-14x⋅x-14x⋅-1-1x-1⋅-1)⋅-1=0⋅-1

Simplify and combine like terms.

Simplify each term.

Multiply x by x by adding the exponents.

Move x.

(-14(x⋅x)-14x⋅-1-1x-1⋅-1)⋅-1=0⋅-1

Multiply x by x.

(-14×2-14x⋅-1-1x-1⋅-1)⋅-1=0⋅-1

(-14×2-14x⋅-1-1x-1⋅-1)⋅-1=0⋅-1

Multiply -1 by -14.

(-14×2+14x-1x-1⋅-1)⋅-1=0⋅-1

Rewrite -1x as -x.

(-14×2+14x-x-1⋅-1)⋅-1=0⋅-1

Multiply -1 by -1.

(-14×2+14x-x+1)⋅-1=0⋅-1

(-14×2+14x-x+1)⋅-1=0⋅-1

Subtract x from 14x.

(-14×2+13x+1)⋅-1=0⋅-1

(-14×2+13x+1)⋅-1=0⋅-1

Apply the distributive property.

-14×2⋅-1+13x⋅-1+1⋅-1=0⋅-1

Simplify.

Multiply -1 by -14.

14×2+13x⋅-1+1⋅-1=0⋅-1

Multiply -1 by 13.

14×2-13x+1⋅-1=0⋅-1

Multiply -1 by 1.

14×2-13x-1=0⋅-1

14×2-13x-1=0⋅-1

14×2-13x-1=0⋅-1

Multiply 0 by -1.

14×2-13x-1=0

14×2-13x-1=0

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=14⋅-1=-14 and whose sum is b=-13.

Factor -13 out of -13x.

14×2-13x-1=0

Rewrite -13 as 1 plus -14

14×2+(1-14)x-1=0

Apply the distributive property.

14×2+1x-14x-1=0

Multiply x by 1.

14×2+x-14x-1=0

14×2+x-14x-1=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(14×2+x)-14x-1=0

Factor out the greatest common factor (GCF) from each group.

x(14x+1)-(14x+1)=0

x(14x+1)-(14x+1)=0

Factor the polynomial by factoring out the greatest common factor, 14x+1.

(14x+1)(x-1)=0

(14x+1)(x-1)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

14x+1=0

x-1=0

Set the first factor equal to 0.

14x+1=0

Subtract 1 from both sides of the equation.

14x=-1

Divide each term by 14 and simplify.

Divide each term in 14x=-1 by 14.

14×14=-114

Cancel the common factor of 14.

Cancel the common factor.

14×14=-114

Divide x by 1.

x=-114

x=-114

Move the negative in front of the fraction.

x=-114

x=-114

x=-114

Set the next factor equal to 0.

x-1=0

Add 1 to both sides of the equation.

x=1

x=1

The final solution is all the values that make (14x+1)(x-1)=0 true.

x=-114,1

Solve using the Square Root Property 13x+1=14x^2